100 words summary

CRIME, ARRESTS, AND PRETRIAL JAIL INCARCERATION: AN EXAMINATION OF THE DETERRENCE THESIS*

STEWART J . D’ALESSIO LISA STOLZENBERG

Florida International University

Using longitudinal data calibrated i n daily intervals and a vector A R M A ( V A R M A ) study design, we investigate the causal relations a m o n g the n u m b e r of crime5 reported t o the police, the frequency of arrest, and the n u m b e r of defendants held in pretrial jail confinement. Results show a lagged negative effect of frequency of arrest on reported crime. A s the n u m b e r of wrests m a d e by police increases, the n u m b e r of index crimes reported t o authorities decreases substantially the f o l - lowing day. Additionally. the analysis reveals N significant positive contemporaneous relationship between criminal activity and arrest levels. N o feedback effects a m o n g the three variables are noted. In s u m , o u r findings add empirical support t o the thesis that the instanta- neous and lagged relationship between crime and clearances are of opposite sign. That is, criniincrl activity increases arrest levels instanta- neously, or at least relatively so, while the negative effect of arrest levels on crime levels transpires m o r e gradually.

A fairly large and diverse body of empirical research accumulated since the late 1960s and early 1970s reports an inverse relationship between arrest certainty and crime rates (Blumstein et al., 1978). Studies con- ducted at the national (Gibbs, 1968), state (Logan, 1975), county (Bailey, 1976; Brown, 1978; Tittle and Rowe, 1974), city (Chamlin, 1991; Chamlin e t al., 1992; Tittle and Rowe, 1974), and census-tract (Kohfeld and Sprague, 1990) levels all show this pattern. However, there are two limita- tions to viewing these findings as unqualified support for the deterrence hypothesis. First, a number of investigators are uncertain as to whether arrest certainty is the cause or the effect of criminal activity (Fisher and Nagin, 1978; Gibbs and Firebaugh, 1990). That is, if certainty of punish- ment and crime rates are related, the causal influence could run in the opposite direction: Criminal activity could influence certainty of punish- ment. There are convincing theoretical expectations for such a relation- ship. For example, it has been argued that high crime rates produce an

* This article is a revised version of a paper presented at the 49th Annual Meeting of the American Society of Criminology, San Diego, November 19-22. 1997. We wish to thank the anonymous reviewers for their valuable comments.

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736 D’ALESSIO AND STOLZENBERG

overload effect, meaning that the state’s ability to capture, convict, and imprison offenders declines as the crime rate rises because of inelastic police resources (Geerken and Gove, 1977). It also has been argued that high crime rates have a desensitizing effect, thereby engendering greater public tolerance of criminal behavior (Greenberg et al., 1979). On the other hand, it is possible that high crime rates increase public fear, which in turn influences the community to expend additional resources on law enforcement and on other formal mechanisms of social control (Becker, 1968). Given the plausibility of these explanations, a compelling theoreti- cal rationale exists for expecting that criminal activity, at least to some degree, influences punishment levels in society.

A second and perhaps more damaging criticism of previous research is whether the inverse relationship between arrest certainty and criminal activity can be attributed to an incapacitative effect. Contrary to the rationale of deterrence theory, the incapacitation thesis suggests that the incarceration of potential offenders reduces the number of crimes perpe- trated against the general public. To date, no study has examined the rela- tionship between arrest certainty and crime, while simultaneously considering pretrial incarceration levels. This neglect is problematic because of the endemic difficulty in disentangling deterrent effects from incapacitative effects (Blumstein et al., 1978). For example, if the crime rate was observed to be lower in an area with a high arrest rate, one can- not determine whether this relationship was due to deterrence or whether it resulted from the incapacitation of pretrial defendants. The primary reason for investigators’ failure to consider the confounding of pretrial incarceration is because of the lack of detailed jail data. Without such data, prior researchers have typically relied on prison incarceration or total jail population as proxy measures of incapacitation. However, because prison incarceration is so far removed in time from the arrest sanction and because total jail incarceration figures include sentenced offenders, it is exceedingly difficult to determine, with any degree of empirical certainty, whether a negative association between arrest levels and criminal activity resulted from an incapacitation effect.

Because all prior studies that tested the deterrence thesis at the macrolevel are vulnerable to one or both of these criticisms, a compelling rationale exists for questioning the validity of their conclusions. Using daily arrest and crime data drawn from the Florida Department of Law Enforcement and pretrial incarceration data drawn from the Orange County Department of Corrections, we reexamine the deterrence ques- tion. Specifically, we employ a vector autoregressive moving-average (ARMA) procedure to examine the relations among criminal activity, arrest levels, and pretrial incarceration levels. Our study improves on pre- vious research in three important ways. First, in contrast to the traditional

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Box-Jenkins’ methodology employed in prior research, the vector ARMA methodology used here allows us not only to assess the contemporaneous and lagged relationship between arrest certainty and criminal activity, but also to directly test for feedback effects. The ability to estimate such effects is important in macrolevel deterrence research because there is rea- son to suspect that the instantaneous and lagged relationship between crime and arrests is of opposite sign (Greenberg and Kessler, 1981). That is, criminal activity most likely affects police activity instantaneously, or at least relatively so, while the effect of police activity on crime probably transpires much more gradually over time. The failure to model both of these differing effects in an analysis can bias parameter estimates (Green- berg and Kessler, 1982).

Second, we include a control for pretrial incarceration in the analysis. Any accurate test of the deterrence thesis must control for pretrial incar- ceration levels because deterrent and incapacitative effects are con- founded. For example, an investigator cannot say that an inverse relationship between arrest levels and crime levels is due to a deterrent effect without controlling for the number of defendants held in pretrial confinement. Likewise, an investigator cannot say that confining defend- ants before trial reduces crime without accounting for the possibility of a deterrent effect.

Finally, we use day as our unit of analysis. Because of ambiguity con- cerning the appropriate lag structure between police activity and crime levels (Loftin and McDowall, 1982), the best way to test for deterrent effects is to calibrate data into the finest temporal aggregation possible (Chamlin et al., 1992). By doing so, it is easier to establish time order. As Granger (1969:430) points out: “In many economic situations an apparent instantaneous causality would disappear if the economic variables were recorded at more frequent time intervals.” By analyzing data calibrated in daily intervals rather than in yearly, monthly, or weekly intervals, we are in a better position to determine which variable, criminal activity or arrest levels, has the more powerful effect on the other, the direction of the effect, and the strength of the effect. Because no other study has incorpo- rated these features in a single inquiry, our research offers a unique oppor- tunity to assess the validity of the deterrence thesis.

BACKGROUND

Although research frequently documents an inverse association between arrest certainty and criminal activity (see Gibbs, 1986), some dis- agreement exists among social scientists as to what such a finding actually means. There are currently three contrasting views of the theoretical processes that explain this relationship: (1) the deterrence thesis, (2) the

D’ALESSIO AND STOLZENBERG

crime-punishment thesis, and ( 3 ) the incapacitation thesis. The first two of these theses debate the causal direction of the association. While the deterrence thesis predicts that relative increases in the certainty of punish- ment reduce crime, the crime-punishment thesis asserts that changes in levels of crime influence punishment levels. By contrast, the incapacita- tion thesis assumes that the number of pretrial defendants confined in jail affects crime rates.

Although the most widely accepted of these three interpretations is probably the deterrence thesis, which proffers that people are free-will actors who engage in criminal activity only after rationally weighing the potential benefits and probable liabilities associated with such activity, many social scientists remain skeptical of results purporting to show deter- rent effects because of the prospect of simultaneity between the certainty of punishment and criminal activity. Although theory concerning the effect of crime rates on punishment certainty is broad and diverse, three fairly distinct perspectives can be distinguished. This classification inevita- bly simplifies some salient theore tical issues, but it does identify the essen- tial distinctions among the perspectives.

One common thesis suggests that organizational efficiency is related to workload. Adherents to this view maintain that because policing is consid- ered a labor-intensive activity (Bordua and Haurek, 1971) and because police resources tend to be relatively inelastic, at least in the short term (McDowall and Loftin, 1986), increases in the crime rate are thought to adversely affect police performance. As crime rates rise, the demand on finite police resources intensifies, lowering the probability of an arrest fol- lowing the commission of a crime. High crime rates are also thought to decrease the state’s ability to prosecute, convict, and incarcerate offenders. Research that has investigated this issue has generally found that increased police workload tends to decrease the certainty of punishment (Liska et al., 1985).

A second perspective argues that crime rates influence public attitudes, which in turn affect law enforcement practices (Greenberg et al., 1979). Two main variants of this argument have been advanced in the literature. One focuses on the desensitizing aspects associated with repeated expo- sure to crime and violence, while the other centers on the public’s concern with rising crime levels. According to Bandura (1973), repeated exposure to either direct or indirect violence has a desensitizing effect on individu- als. Bandura’s claim is consistent with experimental studies showing that frequent exposure to violence, such as watching violent television pro- grams, not only results in a gradual blunting of emotional responses to subsequent displays of aggression (Thomas et al., 1977), but also reduces the speed and willingness of an individual to intervene in the violent dis- putes of others (Drabman and Thomas, 1974).

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A second variant of the public attitude thesis, commonly referred to as public choice theory, maintains that communities respond to rising crime levels by increasing public expenditures for law enforcement and other crime control agencies (Becker, 1968). The allocation of additional resources to law enforcement is thought to reduce crime by amplifying police presence on the street and by raising the probability of an officer being at the scene of a crime. Research findings on the relationship between changes in crime rates and police resources (i.e., police size, police expenditures) are mixed, however. A number of empirical studies find that violent crime rates (Greenberg et al., 1983), property crime rates (Chamlin, 1989), or total crime rates (Land and Felson, 1976) influence police resources, while several other investigators report little evidence that crime rates and police resources are related in any meaningful way (Benson et al., 1994; Greenberg et al., 1985; Loftin and McDowall, 1982; McDowall and Loftin, 1986). Explanations for these divergent findings include simultaneous feedback between police resources and crime rates (Swimmer, 1974), differences in styles of policing (Wilson and Boland, 1978), and the conversion of additional crime control resources to areas that have little direct effect on police performance, such as higher salaries and pensions (Blumstein et al., 1978). Differences in causal mechanisms aside, these predictions provide a more complex view of the relationship between the certainty of punishment and crime rates than deterrence the- ory predicts.

Although most studies have ignored the possibility of reciprocal effects between arrest certainty and criminal activity, some investigators have been mindful of potential causality problems. Aggregate studies of deter- rence typically have relied upon two research strategies to model possible simultaneous effects. The first approach estimates panel models of recip- rocal causation, in which arrest rates and crime rates are stipulated as both cause and effect of each other. Studies that employ this strategy typically include a lagged measure of arrest certainty in the analysis. The second approach uses an autoregressive integrated moving average (ARIMA) time-series methodology, which allows the data to aid in the determination of the appropriate lag structure between arrest rates and crime rates.

The relative lack of correspondence in findings between panel and ARIMA studies is quite striking. Using a multiwave panel model, which allowed for the estimation of both instantaneous and lagged influences, Greenberg et al. (1979) found no significant relationship between arrest rates and crime rates in either direction. They concluded that previous cross-sectional research examining only one-way causation had errone- ously exaggerated the relationship between arrest rates and crime rates. Other panel studies reached similar conclusions (Greenberg and Kessler, 1982; but see Kohfeld and Sprague, 1990; Marvel1 and Moody, 1996).

740 D’ALESSIO AND STOLZENBERG

In contrast to previous panel research, studies that used ARIMA to test the deterrence thesis have generally evinced a strong and statistically sig- nificant inverse lagged relationship between arrest certainty and criminal activity (Chamlin, 1991; Chamlin et al., 1992; but see Chamlin, 1988). Using monthly and quarterly data over 23 years (1967 to 1989), Chamlin et al. (1992) found significant negative relationships between arrest rates and the rates of robbery and auto theft in the monthly data. They also found a deterrent effect for larceny crimes in the quarterly data. In another ARIMA study that examined certainty and crime rates for seven Penn- sylvania cities varying in population size from 5,000 to 2 million, Chamlin (1991) reported support for the deterrence thesis for small cities, with cer- tainty of punishment levels at about 40%.

How might the discrepancy in findings between these two different approaches be explained? One possible explanation for these contradic- tory findings is that the panel research design used by Greenberg and his associates is inappropriate for testing the deterrence thesis because of uncertainty regarding the lag structure between arrest certainty and crime rates (Chamlin et al., 1992). Because researchers currently lack a theory specifying how much time will pass before changes in the certainty of pun- ishment affect crime rates (Loftin and McDowall, 1982) and because empirical research shows both general (Ross, 1984) and specific deter- rence (Sherman et al., 1991) effects to be short-lived, the use of fixed yearly lags in panel studies may have underestimated the importance of arrest certainty in reducing crime. This problem may explain in part why panel studies, in which yearly lags were typically used, tended to find no significant negative effect of arrest certainty on crime rates, while ARIMA studies, in which monthly lags were employed, d o report such an effect.

However, while the findings generated from prior ARIMA studies are clearly informative, it is questionable whether they can be adequately interpreted as strong support for the deterrence thesis. One major short- coming is that the traditional Box-Jenkins methodology does not allow for the estimation of feedback relationships. The use of ARIMA in deter- rence research is predicated on the assumption that the temporal sequenc- ing between arrests and crime provides a sufficient basis for making inferences about causal order. For example, Kohfeld and Sprague (1990) maintain that the police react in time to criminal activity with immediacy, while criminals respond in time to police sanctioning with diffusion and delay. This delay between police activity and crime represents the time needed for information about changes in the certainty of punishment to be disseminated through the criminal population. If police activity and crimi- nal activity are mutually but not simultaneous determined, it is possible to

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disentangle the relationship between arrest rates and crime rates by disag- gregating observations into highly refined temporal units (Kohfeld and Sprague, 1990).

However, as previously discussed, the use of lags to separate out con- temporaneous effects depends heavily upon the calibration of measure- ment units (Granger, 1969). Even if one were to accept the theoretical rationale of a delayed effect of arrest certainty on crime levels, the lagging of a variable does not necessarily eliminate the problem of simultaneity bias (Firebaugh and Beck, 1994:644). Such a bias could still be present if the data were aggregated in large temporal units (Tiao and Wei, 1976). Because current expectations concerning the lagged structure between punishment certainty and criminal activity are not clearly specified in the literature, apart from a general belief that the effect of police activity on crime is probably not instantaneous, the use of quarterly, monthly, and even weekly lags in prior ARIMA research may still have been too large to separate out contemporaneous effects.

The ability to estimate not only lagged, but also instantaneous effects in macrolevel deterrence research is relevant because there is strong reason to suspect that these two effects are of opposite sign (Greenberg and Kess- ler, 1981). That is, the instantaneous effect between crime and arrests is thought to be positive and the lagged effect of arrests on criminal activity is believed to be negative. If crime affects arrest levels contemporane- ously and if police activity has a lagged negative influence on crime levels, any analysis that does not allow for consideration of both of these differ- ential effects must be rejected as inappropriate (Greenberg and Kessler, 1982). Because previous ARIMA analyses only tested for lagged arrest certainty effects, it is questionable whether findings generated from these studies represent the true nature of the arrest-crime relationship accurately.

A second limitation is that prior analyses implicitly assume that any observed inverse relationship between arrest certainty and crime is the result of a deterrent effect. However, this assumption cannot be ade- quately tested without also measuring pretrial incarceration because meas- ures of deterrence and incapacitation are confounded. To date, no study has examined the relationship between arrest certainty and crime, while simultaneously considering pretrial jail incarceration levels. This oversight is surprising, particularly since many arrested individuals are unable to secure release (e.g., bail) before trial. By failing to include a measure of pretrial confinement, previous research may have suggested a greater direct effect of certainty of punishment on crime than is warranted. As Sampson (1986:286) points out: “If the risk of incarceration in jail not only deters crime but also is simultaneously influenced by the crime rate, then estimates of the deterrent effect of sanctions will be biased.”

742 D’ALESSIO AND STOLZENBERG

Though no previous study to our knowledge has specifically controlled for pretrial jail incarceration when examining the effect of arrest certainty on crime, an analysis of homicide and robbery rates in 171 cities by Samp- son (1986) suggests that the risk of jail incarceration influences crime rates. Controlling for several known determinants of crime rates and dis- aggregating crime-specific offending rates by age, race, and sex, Sampson found that police aggressiveness not only had a significant deterrent effect on robbery, but cities with higher risks of jail incarceration had dispropor- tionately lower robbery rates. In a supplemental analysis, he also found that the risk of jail incarceration had a significant inverse effect on bur- glary rates. Although Sampson did not observe a relationship between the risk of jail confinement and homicide rates, his measure of jail incarcera- tion risk is vitiated by the inclusion of convicted offenders, who compro- mise approximately 50% of jail populations (Perkins et al., 1995). Had Sampson’s measure of jail incarceration been more precise, he might have found a stronger effect on homicide rates.

Though Sampson’s study alerted us to the possible crime-reducing effects of jail incarceration, most investigators have either ignored or downplayed the importance of such effects in reducing crime. Some social scientists maintain that an incapacitative effect will be relatively small unless a high proportion of law violators are recidivists, while others assert that the incapacitation thesis can only account for the negative relation- ship between arrest clearance and crime if a relatively fixed pool of poten- tial criminals exists in a given jurisdiction (Zimring and Hawkins, 1995). Despite the hesitancy of some social scientists to consider the possibility of an incapacitative effect, it should not be dismissed summarily. Rhodes (1985) estimates that approximately 10% of those released pretrial in the United States are rearrested by the police. The threat posed by this seem- ingly small number of offenders is substantial when one considers that an estimated 150,000 additional crimes will be committed each year by defendants released prior to trial (Rhodes, 1985).

The purpose of this study is to investigate further the relationship between criminal activity and arrest certainty, correcting for some of the methodological problems encountered in earlier studies. Our focus is on three primary questions. First, does frequency of arrest affect criminal activity? On the basis of the deterrence assumption that people are rational actors who weigh the likely costs and benefits of their behavior before engaging in any given activity, we expect to find an inverse rela- tionship between arrest levels and reported crime. Second, does criminal activity affect arrest levels? It is possible that high crime levels may affect police activity because of an overload effect, a desensitization effect, or a

THE DETERRENCE THESIS 743

punitive effect. Third, if causality runs in both directions, what is the rela- tive magnitude of the effects of arrest frequency on crime and crime on arrest levels?

In addition to analyzing the relationship between arrest frequency and criminal activity, we attempt to determine whether the number of pretrial defendants confined in jail has an effect on crime that is independent of the effect of police activity. Because the number of arrests made by police is reported to be positively related to jail incarceration levels (Welsh et al., 1990) and because research shows that defendants charged with more seri- ous crimes and defendants with more severe prior records are most likely to be detained before trial (Goldkamp, 1983), it is possible that a negative effect observed between arrest frequency and criminal activity is attributa- ble to an incapacitative effect. To address this possibility, we derive maxi- mum-likelihood estimates from a vector ARMA analysis that simultaneously considers the relations among criminal activity, arrest levels, and pretrial jail incarceration levels. We believe that the identifica- tion of the nature and direction of the causal influences among these three variables will enrich understanding of deterrence theory.

DATA

For our research site, we chose to focus on Orange County, Florida. The city of Orlando, which is located in the county, is one of the largest urban centers in the state. Practical considerations limited our analysis to this county. Specifically, w e were constrained by the availability of pre- trial incarceration data calibrated in daily intervals. In contrast to other counties around the country, Orange County maintains comprehensive and reliable jail data that are sufficiently detailed to enable us to disaggre- gate the daily number of persons confined in the county by pretrial and sentenced defendant classification level. The data encompass a 184-day period, from July 1, 1991, to December 31, 1991.

Though county may be the most appropriate level of analysis of the pro- cess of jail incarceration, since jail construction, policies, and operations affecting pretrial incarceration are developed and implemented at the county level, some writers argue that aggregations smaller than county or city are most appropriate for testing the deterrence thesis. For instance, Bursik et al. (1990) suggest that the transmission of information regarding changes in the certainty of punishment are more likely to be enhanced by the properties of neighborhoods than by those of larger aerial aggrega- tions. However, while it seems reasonable to assume that people are influ- enced more by the punishment levels of more immediate social units, we believe that this position has been overstated in the literature. First, an inverse relationship between arrest certainty and criminal activity has

744 D’ALESSIO AND STOLZENBERG

been observed at many different levels of aggregation (see Gibbs, 1986). Second, it is debatable whether being receptive to social communication regarding changes in police activity is conditioned better by smaller geo- graphical aggregations or by other factors such as the motivation of the individual offender (Sprague, 1982). Third, some social scientists question whether friendship networks are actually circumscribed by bounded geo- graphic areas. For example, Fischer (1982) and Wellman and Wortley (1990) argue that acquaintances, friends, and kin need not necessarily live nearby to be an important element of an individual’s personal network. These authors argue that the frequent practice of limiting personal net- works to bounded geographic entities is not really appropriate since the development of effective and affordable transportation and communica- tion networks makes long-distance relations possible and commonplace.

Our measure of criminal activity consisted of seven reported index crimes: willful homicide, forcible rape, robbery, aggravated assault, bur- glary, larceny-theft, and motor vehicle theft. The crime of arson was excluded from the analysis because of problems with incomplete reporting.

The debate about which measure to use in an analysis-number of arrest made by police or an arrest certainty measure-remains unresolved. Jacob and Rich (1981, 1982) believe that the raw number of arrests is the appropriate measure of arrest certainty, whereas Wilson and Boland (1978, 1982) maintain that risk of apprehension should be measured as a ratio (i.e., the number of arrests made by police divided by the number of crimes reported to police). We follow Jacob and Rich in using the fre- quency of arrests made by police as our measure of arrest certainty. Our use of this measure is based o n the theoretical rationale that because a criminal’s behavior is reported to be based on fairly crude perceptions of events (Cornish and Clarke, 1986), it is most likely that he or she is sensi- tive to the relative frequency of the arrest sanction rather than to the mar- ginal probability of arrest (Kohfeld and Sprague, 1990). Additionally, Gibbs and Firebaugh (1990) suggest that there might be a problem with what they term ”ratio correlation bias.” They maintain that because the arrest certainty measure (i.e., arrestdcrimes) and the dependent variable (i.e., crimes/population) used in deterrence studies have common terms and because these common terms are likely to be measured with error, it is possible that any observed inverse correlation between these two ratio variables may be spurious.

The third variable of interest, pretrial jail incarceration, is measured as the daily number of pretrial defendants incarcerated in jail in Orange County. Drawing from the literature on incapacitation, we expect that the number of pretrial defendants confined in jail will be inversely related to reported crime, net of the effect of the number of arrests made by police.

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The means, standard deviations, and graphs for these variables are presented in Table 1 and Figures 1 to 5.1

Table 1. Descriptive Statistics

Mean S.D. Minimum Maximum ~- Variable

Number of Reported Crimes 169.10 24.15 98.00 240.00 Number of Arrests 53.53 22.36 8.00 104.00 Pretrial Jail Incarceration 1,493.89 66.82 1,331.00 1,651.00 Total Jail Incarceration 3,396.46 116.88 3,147.00 3,634.00 Arrest Certainty .31 .13 .06 .57

METHOD OF ANALYSIS

We used vector ARMA to estimate the relations among criminal activ- ity, arrest levels, and pretrial incarceration levels. Although primarily employed by statisticians and economists, vector ARMA has been used by a few sociologists to examine trends in school victimization (Parker et al., 1991) and to investigate the relationship between alcohol treatment and cirrhosis mortality (Holder and Parker, 1992). Vector ARMA is a fully recursive statistical procedure, which allows us to test for contemporane- ous, lagged, and feedback relationships among two or more variables. Formally, the vector ARMA model is described as: $ ( B ) Z t = e(B)E,, where 4 is a matrix of autoregressive parameters, 8 is a matrix of moving-average parameters, 2, is a stationary vector of time series containing n observa- tions, and E, is a vector of random shocks that are independently, identi- cally, and normally distributed with a zero mean and stable variance.

The methodology for constructing a vector ARMA model consists of three stages: (1) tentative model specification, in which sample cross-cor- relation and partial cross-correlation matrices are used to specify the order of the vector ARMA process; (2) estimation, in which efficient parameter estimates are obtained by maximizing the likelihood function; and (3) diagnostic checking, in which model deficiencies are identified by a cross- correlation analysis of the residual series.

To estimate our model, we used the MTS software package from Auto- matic Forecasting Systems (Reilly, 1986). The identification routine in MTS computes and plots sample autocorrelation matrices and a partial lag correlation matrix. These matrices allow us to identify the appropriate AR and MA orders. In a VARMA (p,q) model, p is the number of

1 . The means and standard deviations for each of the variables suggest that a sufficient degree of variability exists to expect modest effects to emerge in the analysis.

746 D'ALESSIO AND STOLZENBERG

Figure 1. Number of Reported Crimes, by Day, July 1, 1991-December 31, 1991 ( N = 184)

Number 250 1

autoregressive parameters, and q is the number of moving-average param- eters. Once the model is identified, the MTS program uses a moment esti- mation routine (conditional least squares) to estimate the maximum- likelihood parameters (Spliid, 1983). If the estimated model fits well, the residual autocorrelations for the model will be small and weakly related (Tiao and Box, 1981).

The relations among the variables of interest can be assessed in the fol- lowing manner. First, if the matrices for @ ( B ) and 8 ( B ) are lower triangu- lar, it would suggest that the variables in the model are not causally related in the sense of Granger (1969). Second, if the matrices for @ ( B ) and 8 ( B ) are block triangular, it would indicate the existence of a unidirectional relationship. Finally, if an off-diagonal value in the error correlation matrix ( C ) is statistically significant, it would suggest an instantaneous relationship between two variables at the zero lag.

RESULTS PRIMARY ANALYSIS

Initially, we analyzed each of the three series separately. Unit root tests, following the procedure advocated by Dickey et al. (1986), led us to analyze first differences of each of the three series. However, while the augmented Dickey-Fuller tests indicated that each of the univariate series

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Figure 2. Number of Arrests, by Day, July 1, 1991-December 31, 1991 ( N = 184)

Number

100

80

60

40

20

1 11 21 31 41 51 61 71 81 91 101 111 121 131 141 151 161 171 181

Day

was nonstationary, it is possible that a linear combination of two or more of the series was stationary. Such a situation is referred to as cointegra- tion. If two or more of the series are cointegrated, differencing is not rec- ommended. We tested for the presence of cointegration using the procedure suggested by Engel and Granger (1987). Specifically, we com- puted three regressions of the form:

i = l ; i # j

('j = 1, . . ., 3). We then estimated augmented Dickey-Fuller tests on the residuals(&,,) of each of the regressions. Our results indicated that first differencing was appropriate since none of the series appeared to be cointegrated.

Table 2 reports the maximum-likelihood estimates for a VARMA (1,l) model. The residuals for this specification satisfied all the diagnostic requirements suggested by Tiao and Box (1981) to ensure model ade- quacy.2 Several interesting findings emerge from inspection of the autoregressive (5) and moving-average ( e ) matrices. First and most

2. A visual inspection of the autocorrelation and the partial lag correlation matri- ces suggested a seasonal component in the reported crime series. Criminal activity on Sundays was significantly lower than on the other six days of the week. To account for

748 D'ALESSIO AND STOLZENBERG

Figure 3. Pretrial Jail Incarceration, by Day, July 1, 1991-December 31, 1991 ( N = 184)

1700

1650

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1550

1500

1450

1400

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1300

important, we observe a negative and statistically significant delayed effect of frequency of arrest on criminal activity (& < 0). As the number of arrests made by police for index crimes increases, criminal activity decreases substantially the following day. This finding provides empirical evidence for the theoretical arguments articulated by proponents of deter- rence theory.

Second and contrary to predictions derived from the incapacitation the- sis, our findings do not lend credence to the importance of pretrial jail confinement as a factor in reducing either crime fi13 = 0 and a,, = 0) or arrest levels (&, = 0 and 8,, = 0). Although we suggested previously that crime and arrest levels may be inversely related as a result of an incapaci- tation effect, our results do not bear this prediction out. The most salient predictor of current pretrial jail incarceration levels is past levels (& > 0 and e,, > 0). Somewhat surprisingly, our analysis demonstrates that the daily number of arrests made by police is inconsequential in determining pretrial incarceration levels ($32 = 0 and e,, = 0). Although previous

this systematic difference, we included a dummy coded variable (1 = Sunday, 0 = other- wise) in the analysis as a statistical control. As expected, this seasonal variable had a strong effect on criminal levels.

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Figure 4. Total Jail Incarceration, by Day, July 1, 1991-December 31, 1991 ( N = 184)

Number 3700

3600

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3400

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3100 1 11 21 31 41 51 61 71 81 91 101 111 121 131 141 151 161 171 181

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research assumed that police activity was important for understanding var- iations in jail incarceration levels, our analysis undermines this assump- tion. In addition, criminal activity has no salient causal effect on pretrial jail incarceration when preexisting incarceration trends are taken into account (& = 0 and e,, = 0). The weak influence of both arrest and crime levels on pretrial incarceration levels is probably attributable to our reli- ance on vector ARMA, which is generally considered to be a conservative statistical procedure. Our results also show that criminal activity has no lagged effect on arrest levels (& = 0 and & = 0).

A third interesting finding is that an examination of the error correla- tion matrix (2) reveals a positive, contemporaneous relationship between criminal activity and arrest levels. As previously discussed, a contempora- neous relationship between components of a vector series can be modeled through the off-diagonal elements of the error correlation matrix. Using the information provided in this matrix, w e estimated the correlation between the residuals for crime and arrest frequency at the zero lag to be .16. Although this correlation is somewhat small in magnitude, it is still statistically significant at the .05 level of analysis. In contrast, the residual correlations at the zero lag between criminal activity and pretrial incarcer- ation and between arrest frequency and pretrial incarceration are not of substantive importance. Our finding of an instantaneous relationship

750 D'ALESSIO AND STOLZENBERG

Figure 5. Arrest Certainty, by Day, July 1, 1991-December 31, 1991 ( N = 184)

Ratio (ArrestKrime)

0.6

0.5

0.4

0.3

0.2

0.1

1 11 21 31 41 51 61 71 81 91 101 111 121 131 141 151 161 171 181

Day

between criminal activity and arrest levels tends to cast doubt on the argu- ment that increased police workload reduces certainty of punishment. Rather it appears that rising crime levels, at least in the short term, are increasing the number of arrests made by police.

However, it is important to recognize that the contemporaneous rela- tionship depicted in Table 2 is not entirely incompatible with deterrence theory. After all, a contemporaneous relationship between two variables might be (1) unidirectional (i.e., the association is entirely attributable to the effect of one of the variables upon the other, (2) bidirectional (i.e., each variable affects the other significantly and equally), (3) predominant (i.e., each variable affects the other significantly but the effect of one is greater than the effect of the other, or (4) countervailing (i.e., the effect of one on the other is positive while the effect of the second variable on the first is negative). For example, it is entirely possible that criminals respond to changes in police activity within a 24-hour period. Thus, although we calibrated the data into the finest interval possible so as to better deter- mine causality, w e cannot definitely say on the basis of our analysis whether this contemporaneous relationship was solely the result of police reacting to criminal activity. What we can say, however, is that our finding of a contemporaneous relationship between crime and arrest levels lends

THE DETERRENCE THESIS 75 1

Crime

Arrests

Pretrial

Table 2. VARMA Maximum Likelihood Estimates of the Relations Among Crime, Arrests, and Pretrial Jail Incarceration

. -.219 (3.01)

0 . 0 ,419

Crime Arrests Pretrial

,739 . 0 ,838

(11.31) . ,799 (4.71)

--- (9.53)

z x 102 Crime Arrests Pretrial ---

I 4.018

,551 2.725

,075 .007 ,094

NOTE: t score in parentheses. The results are presented in matrix form. The significant coefficient in the (1,2) position indicates that arrest levels influence crime levels at lag -1. If the coefficient in the (2.1) position was statistically significant, it would indicate that criminal activity affects arrest levels at lag -1. If the coefficients in the (1,2) and the (2.1) positions were both significant, it would indicate that there was feedback between crime levels and arrest levels at lag -1. Because VARMA uses an iterative process to derive parameter estimates, only the s i w c a n t coefficients are reported in the final model. The results of the preliminary iterative stages of each of the VARMA analyses conducted in this study can be obtained from the authors on the request.

more support to the thesis that criminal activity is affecting arrest levels than to the reverse.

SUPPLEMENTAL ANALYSES

We conducted two supplemental analyses to ensure that our original findings remained robust across different specifications. First, because an anonymous reviewer thought it prudent to determine whether our findings would vary depending on the incapacitation measure employed, we esti- mated a separate vector ARMA equation using total jail incarceration rather than pretrial jail incarceration as one of our three variables of theo- retical interest. The results of this analysis, which are presented in Table 3, are nearly identical to the findings generated in our original analysis. The effects of each of the variables of interest, or lack thereof, remained stable. We again observed a contemporaneous and a lagged relationship between criminal activity and frequency of arrest. No substantive relationship between total jail incarceration and criminal activity was noted. In fact, when we considered total rather than pretrial incarceration, the magnitude of the incapacitative effect decreased. At the zero lag, for example, the correlation between criminal activity and pretrial incarceration was .13. In contrast, the contemporaneous relationship between criminal activity and total jail incarceration was .11. The most likely explanation for this reduced effect is that the total jail incarceration measure is vitiated b y the inclusion of offenders held for other counties, state offenders, federal offenders, and a variety of other types of offenders. As a consequence,

752 D’ALESSIO AND STOLZENBERG

-.219 ’ (3.01)

0 e .

. . .

one might expect total jail incarceration to have a weaker overall effect on criminal activity than pretrial jail incarceration.

.

Table 3. VARMA Maximum Likelihood Estimates of the Relations Among Crime, Arrests, and Total Jail Incarceration

Crime

Arrests

Jail

a, z x 102 Crime Arrests Jail

,739

0 ,838 (1 1.31)

--- (9.52)

. . .

Crime Arrests Jail --- ’ 4.022

.555 2.124

,098 ,076 ,184

NOTE: t score in parentheses. Additionally, if we carried out the autoregressive and moving- average coefficients for the crime and arrest variables more than three decimal places, they would be slightly different from the same coefficients reported in Table 2.

A second analysis was also conducted using an arrestkrime ratio varia- ble as our deterrence measure. This ratio variable was created by dividing arrest frequency by the number of crimes reported to police. The robust- ness of the results for this analysis, presented in Table 4, is clear. The lagged effect of the arrestkrime ratio variable on criminal activity is large in magnitude and of substantive importance. This finding buttresses the contention that current police activity is a salient predictor of future crime levels. Visual inspection of Table 4 also shows an instantaneous relation- ship between certainty of punishment and crime levels, but the sign of the coefficient is negative rather than positive. The reason that the sign of the coefficient for arrest certainty changed direction is not clear since “the vector ARMA model is careful not to attribute contemporaneous relation- ships to effects in either direction” (Heyse and Wei, 1985:lSO). What is clear, however, is that the causal processes linking crime and arrests appear to be contingent on time. That is, one process appears to operate instantaneously, or relatively so. and the other seems to operate more gradually. Taken in total, our initial results-and the results of our supple- mental analyses-all tell the same story: There is strong evidence that police activity is an important factor in determining future crime levels, whereas both pretrial and total jail incarceration appear to be less salient.

CONCLUSION We began this article by noting that although a number of empirical

studies have reported an inverse association between arrest certainty and criminal activity, several social scientists have raised important questions concerning the bearing of this relationship on postulated processes. One

THE DETERRENCE THESIS 753

' 3.989

-.364 ,916

,072 -.016 ,095

Table 4. VARMA Maximum Likelihood Estimates of the Relations Among Crime, Arrest Certainty, and Pretrial Jail Incarceration

Crime

Certain

Pretrial

91 el z x 102 Crime Certain Pretrial Crime Certain Pretrial Crime Certain Pretrial ---

I -.122 -.373 (2.04) (2.86)

. ,416 (2.68)

--- ' ,686

,764 (10.27)

,795

(6.97)

NOTE t score in parentheses.

question centers on the reciprocal nature of the arrest-crime relationship. Does police activity influence crime levels, or does criminal activity affect arrest levels? Another question concerns the extent to which any inverse relationship between arrest levels and criminal activity can be attributed to an incapacitative effect.

Although no single study can definitely answer these complicated ques- tions, our analysis attempted to provide a more accurate appraisal of the relationship between criminal activity and arrest levels than previously available. Using daily data and a vector ARMA statistical procedure, we tested for instantaneous, lagged, and feedback effects among crime levels, arrest levels, and pretrial incarceration levels. Results showed that con- trolling for pretrial incarceration levels, the number of daily arrests made by police and a certainty of punishment measure had delayed, negative effects on criminal activity. These findings are in accord with the tenets of deterrence theory.

Findings from the vector ARMA analyses also lend credence to the the- oretical importance of criminal activity as a factor in determining arrest levels. Rather than responding solely to the number of arrests made by police, criminal activity and arrest levels were correlated at the zero lag. Taken in total, these results speak to the validity of the claim made by previous investigators that the causal processes linking crime and arrests are contingent on time. That is, it appears that criminal activity has a rela- tively immediate impact on arrest levels, while the effect of police activity on crime levels seems to transpire more gradually (Greenberg and Kess- ler, 1982; Kohfeld and Sprague, 1990).

These findings, tentative though they be, have important theoretical implications for understanding the deterrence process. First, the evidence presented here, which is based on a more sophisticated analysis than used

754 D'ALESSIO AND STOLZENBERG

in previous studies, suggests that using either frequency of arrest or a cer- tainty of punishment ratio measure does not really make a great deal of difference in testing for deterrent effects since both measures produced nearly identical results. Second and somewhat surprisingly, it took only one day for a deterrent effect to manifest itself. The question that remains unanswered is why a one-day lag? Despite the importance of information diffusion in the study of general deterrence, no studies to our knowledge have assessed empirically the speed at which information regarding changes in police activity is transmitted through the population. Even so, our finding of a one-day lag is consistent with the operation of news diffu- sion processes described by a number of researchers.

The rapid speed at which important news stories are disseminated through the population is one of the most consistent findings in the com- munication literature. Across a variety of samples, methods, and news- worthy events, researchers have repeatedly shown that news regarding events such as the death of Franklin D. Roosevelt (Miller, 1945), the attempted assassinations of President Ronald Reagan (Gantz, 1983) and Governor George Wallace (Steinfatt et al., 1973), and the Challenger space shuttle disaster (Mayer et al., 1990) spreads rapidly through the pop- ulation. In a meta-analysis of the results of 34 news diffusion studies, cov- ering 45 years, from 1945 to 1990, Basil and Brown (1994) found that most people surveyed were made aware of a given news story within a 24-hour period. This pattern of rapid diffusion of information remained robust despite factors such as type of news story, geographic location, and demo- graphic characteristics of respondents. Person-to-person communication was frequently the primary source of information rather than newspapers, radio, or television. Even more relevant to deterrence theory is that infor- mation regarding a "potential risk" tends t o be disseminated much more rapidly by individuals than other types of information (Weenig and Mid- den, 1991).

These studies' findings have important implications, not only because they have been replicated numerous times and across different types of news stories, but because they bear directly on current debates regarding the timing of deterrent effects. Because existing theory has failed to fur- nish any basis for either the timing or longevity of deterrent effects, researchers have generally relied on yearly, quarterly, monthly, or weekly data to test for deterrent effects. However, based on the findings presented here and on the findings reported in the news diffusion litera- ture, it appears that this practice may be theoretically unjustifiable. There is every reason t o assume that the dissemination of information is occur- ring much more rapidly than previously thought. Thus, if one accepts the argument that a short delay exists between changes in police activity and

THE DETERRENCE THESIS 755

changes in crime levels, one must reject the use of long lags to test for deterrent effects.

Another interesting finding was the lack of any empirical evidence sup- porting the incapacitation thesis. Both pretrial and total jail incarceration levels had no statistically discernible effect on reported crime levels. It is fruitful to ask why the hypothesized linkage was not found. We offer two plausible explanations that warrant consideration. One possibility is that because current practices already confine a substantial proportion of high- risk offenders behind bars, a diminishing marginal return can be expected by further increases in incarceration levels.3 This argument has been articulated rather convincingly by a number of social scientists (Canela- Cacho et al., 1997; Zimring and Hawkins, 1995). A second explanation for our null finding relates to the prevalence of juvenile crime and the confin- ing of juveniles in local jails. Juveniles currently account for a large per- centage of the serious crime committed in the United States. For example, while juveniles between the ages of 10 and 17 constituted about 25% of the population, they accounted for 19% of the arrests for violent crimes and 35% of the arrests for property crimes in 1994 (Federal Bureau of Investigation, 1995). For some crimes such as homicide, the situation is even more disturbing. Over the past decade the rate of homicide commit- ted by teenagers between the ages of 14 to 17 has more than doubled. It increased more than 170%, from 7.0 per 100,000 in 1985 to 19.1 in 1994 (Fox, 1996). However, while juveniles are responsible for a sizable pro- portion of the crime experienced in society, they are typically not confined in jail before trial. For example, although juveniles accounted for over 9% of the arrests in Orange County during the study period, they comprised less than 1% of the pretrial jail population.4 Thus, because juveniles are usually not confined in local jails, it seems likely that pretrial jail incarcera- tion levels would have relatively little effect on reducing juvenile crime.

However, certain caveats must be considered. First, the findings reported here must be replicated with other data sets before they can be accepted without question. Because this study focused on one large county, it is somewhat difficult to draw inferences about the general- izability of our findings. As a consequence, future investigators should consider replicating this analysis in other jurisdictions. The more fre- quently such research is conducted, the greater confidence can be placed in the generalizability of our findings to different times and places.

Second, there will always remain a question as to whether the evidence

3. Approximately 3,572 offenders from Orange County were confined in state

4. However, approximately 1,743 juvenile offenders were detained in juvenile prisons on June 30, 1997.

detention facilities in Orange County during fiscal year 1996-97.

D’ALESSIO AND STOLZENBERG

presented here suffices to discredit the incapacitation thesis. For example, one could make a reasonable argument that a longer period of observation would be needed to support an incapacitative effect. Although it would have been desirable to extend the period of analysis, difficulties in obtaining the data precluded extending the series.

Third, the contemporaneous relationship between criminal activity and arrest levels should be disentangled in future empirical work. Specifying more precisely the underlying causal mechanisms of this association will lead to a better understanding of the deterrence process. Although such an exploration can be addressed within the analytic framework presented here, the data necessary for such an undertaking must be calibrated into even finer temporal units. Unfortunately, most analysts will probably find it difficult to obtain data calibrated in hourly intervals. Nonetheless, the work presented here has come considerably closer to disentangling deter- rent effects from both saturation and incapacitative effects. Additionally, the analytic procedure employed here has the potential to advance under- standing of a wide range of similar phenomena about which contempora- neous, lagged, and feedback relationships are theorized to occur.

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Stewart J. D’Alessio is an Assistant Professor in the School of Policy and Manage- ment at Florida International University. He received his Ph.D. in criminology from Florida State University. He also served previously as a captain in the U.S. Army, and he participated in “Operation Just Cause” and “Operation Desert Storm.” His current research focuses on deterrence theory.

Lisa Stolzenberg is an Assistant Professor in the School of Policy and Management at Florida International University. She also received her Ph.D. in criminology from Flor- ida State University. Her publications have appeared in the American Sociological Review, Criminology, Journal of Criminal Justice, Justice Quarterly, and a variety of other scholarly journals. She is also the co-editor of Criminal Courts in the 21st Cen- tury, which is forthcoming from Prentice-Hall.

762 D’ALESSIO AND STOLZENBERG